The magnetization process of the \(S=1/2\) distorted diamond spin chain with the Dzyaloshinsky–Moriya interaction is investigated using the numerical diagonalization of the finite-size cluster. Although the spin gap cannot be observed by ESR because of the spin conservation law, it is sometimes possible to detect due to the Dzyaloshinsky–Moriya interaction. When the spin gap at the 1/3 magnetization plateau of the natural mineral azurite is possibly observed by ESR, the selection rules with respect to the relative angle between the external magnetic field and the Dzyaloshinsky–Moriya interaction are theoretically predicted.
